TB Consider the ordered bases B = [M]B = -3 4 (8 96382)- 0 0 -2 -3 1 0 4 2 c=3² 39.6 * 3) ) for the vector space V of upper triangular 2 x 2 matrices. 0 -3 0 2 0 a. Find the transition matrix from C to B. 3 E = c. Find M. M = -3 0-2 b. Find the coordinates of M in the ordered basis B if the coordinate vector of M in C is 2 [M]c = 1 3 and

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.1: Inner Product Spaces
Problem 4AEXP
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TB
-2
-3 1
4
2
c=2²36 96 31
0 -3 0
2
a. Find the transition matrix from C to B.
3
E
=
[M]B =
-3
4
-3
- 96 382) -
36
and
0
0
0-2
Consider the ordered bases B =
b. Find the coordinates of M in the ordered basis B if the coordinate vector of M in C is
2
[M]c = 1
3
c. Find M.
M =
) for the vector space V of upper triangular 2 x 2 matrices.
Transcribed Image Text:TB -2 -3 1 4 2 c=2²36 96 31 0 -3 0 2 a. Find the transition matrix from C to B. 3 E = [M]B = -3 4 -3 - 96 382) - 36 and 0 0 0-2 Consider the ordered bases B = b. Find the coordinates of M in the ordered basis B if the coordinate vector of M in C is 2 [M]c = 1 3 c. Find M. M = ) for the vector space V of upper triangular 2 x 2 matrices.
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